基于Laplace分布的两类统计模型的参数估计

发布时间：2018-06-20 17:17

本文选题：Laplace分布 + 一元线性测量误差模型　；参考：《山西师范大学》2017年硕士论文

【摘要】：Laplace分布是统计学中很重要的一类分布.本文基于Laplace分布,分别研究了两类统计模型的参数估计问题.具体内容如下:1.当测量误差服从Laplace分布时,本文基于Laplace分布的Tweedie型公式和回归校正方法给出了一元线性测量误差模型参数的一种新的估计方法,并在一定的正则条件下,证明了所给估计的大样本性质,包括相合性和渐近正态性.模拟研究表明在有限样本下,本文所提出估计是有效的,且在大多数情况下优于已有的一些估计.2.Laplace分布可以表示成正态分布和一个与指数分布相关分布的组合,且与最小一乘估计有紧密的联系.基于最小一乘估计的稳健性,本文假定随机误差服从Laplace分布,给出了响应变量右删失的混合线性回归模型参数的稳健估计.模拟研究和实例表明,本文所提出的估计比MLE和EM具有更好的稳健性.
[Abstract]:Laplace distribution is an important kind of distribution in statistics. In this paper, we study the parameter estimation of two statistical models based on Laplace distribution. The details are as follows: 1. In this paper, a new method for estimating the parameters of a linear measurement error model is presented based on the Tweedie type formula of Laplace distribution and the regression correction method when the measurement error is obtained from the Laplace distribution, and under certain regular conditions, a new method for estimating the parameters of the linear measurement error model is presented in this paper. It is proved that the large sample properties of the given estimates include consistency and asymptotic normality. Simulation results show that the proposed estimators are valid in finite samples, and in most cases are superior to some existing estimation.2. Laplace distribution can be expressed as a combination of normal distribution and a distribution related to exponential distribution. And it is closely related to the least one multiplication estimate. Based on the robustness of the least one multiplication estimator, this paper assumes that the random error is distributed from the Laplace distribution, and gives the robust estimation of the parameters of the mixed linear regression model with the right censored response variable. Simulation results and examples show that the proposed estimation is more robust than MLE and EM.
【学位授予单位】：山西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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